带运输考虑的多阶段动态可重入混合流水车间调度

可重入混合流水车间调度允许一个工件多次进入某些加工阶段,它广泛出现在许多工业制造过程中,如半导体制造、印刷电路板制造等.本文研究了带运输时间的多阶段动态可重入混合流水车间问题,目标是最小化总加权完成时间.针对该问题,建立了整数规划模型,进而基于工件解耦方式提出了两种改进的拉格朗日松弛(LR)算法.在这些算法中,设计了动态规划的改进策略以加速工件级子问题的求解,提出了异步次梯度法以得到有效的乘子更新方向.测试结果说明了所提出的两种改进算法在解的质量和运行时间方面均优于常规LR算法,两种算法都能在可接受的计算时间内得到较好的近优解.     

柔性作业车间生产计划与调度集成优化求解策略

针对柔性作业车间(Flexible job-shop, FJS)生产计划(Production planning, PP)与调度紧密衔接的特点, 建立了生产计划与调度集成优化模型. 模型综合考虑了安全库存、需求损失及工件加工路线柔性等方面因素. 提出了一种基于拉格朗日松弛(Lagrangian relaxation, LR)的分解算法, 将原问题分解为计划子问题与调度子问题. 针对松弛的生产计划子问题, 提出一种新的费用结构, 以保证生产计划决策与实际情况相符, 并设计了一种变量固定—松弛策略与滚动时域组合算法进行求解. 对于调度子问题中的加工路线柔性问题, 提出了一种新的机器选择策略. 通过数值实验验证了模型与算法的有效性.     

冷链物流越库调度的拉格朗日松弛算法

为了提高冷链物流的运输效率,解决越库在冷链物流中的应用问题,提出了基于拉格朗日松弛算法的冷链物流的越库调度方法.首先进行了问题域的描述并做出了具体假设,基于问题域以最小化卡车等待时间和越库内部运输成本为目标,建立越库调度的整数规划数学模型.然后,提出了针对越库调度模型的拉格朗日松弛算法,松弛复杂约束后根据决策变量将松弛问题分解为若干子问题,采用次梯度算法求解松弛模型.最后,对各种不同规模的越库模型进行仿真实验,并与传统的贪婪算法进行对比,结果表明,所提出的调度算法适用于问题的求解,并可以在较短时间内获得良好的近优解.     

装配线物料搬运的拉格朗日松弛算法

为提高汽车制造企业混流装配线的运行效益,提出了基于看板模型的多封闭循环路径多载量小车物料配送调度方法—–装配线物料配送调度的拉格朗日松弛算法.首先对问题域进行了描述并做出了具体假设,以最小化配送系统总成本为目标,建立了混合整数规划模型.在此基础上,针对该模型提出了两种算法—–次梯度和随机步长拉格朗日松弛算法,将松弛问题分解为两个决策子问题分别进行求解.仿真实验表明提出的两种调度算法均适用于该研究问题域,并在求解时间及稳定性上表现出良好的性能.     

航天测控调度分枝定界算法

通过分析航天测控调度问题的测控需求,建立了航天测控调度整数规划模型,引入了拉格朗日松弛思想并与分枝定界算法结合,设计了基于拉格朗日松弛的分枝定界算法求解航天测控调度问题。通过对两个场景的仿真实验,得到了两个场景的航天测控调度问题最优值,验证了基于拉格朗日松弛的分枝定界算法的有效性。     

可延迟供货的冷轧生产库存问题之建模与优化

本文针对可延迟供货的冷轧生产系统,建立了以最小化库存成本、拖期惩罚和启动成本为目标的多阶段生产库存模型,模型中充分考虑了工序不允许停机的情况以及计划与调度之间的一致性问题.同时开发了基于变量分离的有效拉格朗日松弛求解算法,并使用120个基于实际生产数据的算例进行了仿真实验,计算结果显示该算法能够在合理的时间内得到高质量的解.     

汽车同步装配线生产计划与调度集成优化汽车同步装配线生产计划与调度集成优化

为克服传统的"自顶向下"方式下生产计划与调度不协调的缺陷,针对汽车同步装配线,构造了生产计划与调度集成优化混合整数规划模型,并采用拉格朗日松弛法将其分解为批量计划及调度等子问题.将调度子问题转化为与时间相关的旅行商问题,并采用dynasearch算法求解.对于拉格朗日对偶问题,采用均衡方向策略法求解.仿真实验结果验证了模型及算法的有效性.     

带最小批量约束的计划问题及其拉格朗日松弛算法

针对一类带最小批量约束的计划问题, 提出了基于拉格朗日松弛策略求解算法. 通过拉格朗日松弛策略, 将原问题转为一系列带最小批量约束的动态经济批量W-W(Wagner-Whitin)子问题. 提出了解决子问题且其时间复杂度O(T³)的最优前向递推算法. 对于拉格朗日对偶问题, 用次梯度算法求解, 获得原问题的下界. 若对偶问题的解是不可行的, 通过固定装设变量, 求解一个剩余的线性规划问题来进行可行化处理. 最后, 数据仿真验证了算法的有效性.     

基于总加权完成时间的可重入混合流水车间调度问题

研究以最小化总加权完成时间为目标的可重入混合流水车间调度问题(RHFS-TWC),并构建问题的整数规划模型.根据模型的特点,设计基于二维矩阵组的调度解编码方案,结合NEH启发式算法确定工件初始加工顺序,生成高质量初始调度解群.为避免算法陷入早熟及扩大解的搜索空间,给出IGA的遗传参数自适应调整策略,最终形成NEH-IGA融合求解策略.针对不同规模问题分别用传统GA、基于遗传参数自适应调整的IGA、NEH启发式、NEH-IGA算法进行仿真测试,仿真结果表明NEH启发式和遗传参数自适应动态调整策略的引入有效改善了原有GA的求解能力,NEH-IGA算法在求解RHFS-TWC问题方面优势明显.     

离散事件和混杂系统的调度控制*

从系统控制的角度研究了离散事件和混杂系统的调度问题.回顾了我们以前的工作,包括拉格朗日松弛技术,分布实时set-up 调度,随机和可维修系统的调度,神经网络及其它搜索技术的调度,制造系统和库存系统的安全点策略,以及并行处理系统的一些新的启发调度规则,等等.然后介绍了可重入生产系统调度控制的一些新结果.可重入生产系统在现代VLSI制造系统中是非常重要的.建立了QBD型模型,并用Neuts的矩阵几何方法求解.用随机搜索方法解决了监测站的设置问题.数值仿真结果证明了这种方法的有效性和适应性.     

Lagrangian relaxation with cut generation for hybrid flowshop scheduling problems to minimize the total weighted tardiness

In this paper, we address a new Lagrangian relaxation (LR) method for solving the hybrid flowshop scheduling problem to minimize the total weighted tardiness. For the conventional LR, the problem relaxing machine capacity constraints can be decomposed into individual job-level subproblems which can be solved by dynamic programming. The Lagrangian dual problem is solved by the subgradient method. In this paper, a Lagrangian relaxation with cut generation is proposed to improve the Lagrangian bounds for the conventional LR. The lower bound is strengthened by imposing additional constraints for the relaxed problem. The state space reductions for dynamic programming for subproblems are also incorporated. Computational results demonstrate that the proposed method outperforms the conventional LR method without significantly increasing the total computing time.     

A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

We investigate the problem of scheduling n jobs in s-stage hybrid flowshops with parallel identical machines at each stage. The objective is to find a schedule that minimizes the sum of weighted completion times of the jobs. This problem has been proven to be NP-hard. In this paper, an integer programming formulation is constructed for the problem. A new Lagrangian relaxation algorithm is presented in which precedence constraints are relaxed to the objective function by introducing Lagrangian multipliers, unlike the commonly used method of relaxing capacity constraints. In this way the relaxed problem can be decomposed into machine type subproblems, each of which corresponds to a specific stage. A dynamic programming algorithm is designed for solving parallel identical machine subproblems where jobs may have negative weights. The multipliers are then iteratively updated along a subgradient direction. The new algorithm is computationally compared with the commonly used Lagrangian relaxation algorithms which, after capacity constraints are relaxed, decompose the relaxed problem into job level subproblems and solve the subproblems by using the regular and speed-up dynamic programming algorithms, respectively. Numerical results show that the new Lagrangian relaxation method produces better schedules in much shorter computation time, especially for large-scale problems.     

An exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times

This study proposes an exact algorithm for the single-machine total weighted tardiness problem with sequence-dependent setup times. The algorithm is an extension of the authors' previous algorithm for the single-machine scheduling problem without setup times, which is based on the SSDP (Successive Sublimation Dynamic Programming) method. In the first stage of the algorithm, the conjugate subgradient algorithm or the column generation algorithm is applied to a Lagrangian relaxation of the original problem to adjust multipliers. Then, in the second stage, constraints are successively added to the relaxation until the gap between lower and upper bounds becomes zero. The relaxation is solved by dynamic programming and unnecessary dynamic programming states are eliminated to suppress the increase of computation time and memory space. In this study a branching scheme is integrated into the algorithm to manage to solve hard instances. The proposed algorithm is applied to benchmark instances in the literature and almost all of them are optimally solved.     

Hybrid discrete differential evolution algorithm for biobjective cyclic hoist scheduling with reentrance

Cyclic hoist scheduling problems in automated electroplating lines and surface processing shops attract many attentions and interests both from practitioners and researchers. In such systems, parts are transported from a workstation to another by a material handling hoist. The existing literature mainly addressed how to find an optimal cyclic schedule to minimize the cycle time that measures the productivity of the lines. The material handling cost is an important factor that needs to be considered in practice but seldom addressed in the literature. This study focuses on a biobjective cyclic hoist scheduling problem to minimize the cycle time and the material handling cost simultaneously. We consider the reentrant workstations that are usually encountered in real-life lines but inevitably make the part-flow more complicated. The problem is formulated as a biobjective linear programming model with a given hoist move sequence and transformed into finding a set of Pareto optimal hoist move sequences with respect to the bicriteria. To obtain the Pareto optimal or near-optimal front, a hybrid discrete differential evolution (DDE) algorithm is proposed. In this hybrid evolutional algorithm, the population is divided into several subpopulations according to the maximal work-in-process (WIP) level of the system and the sizes of subpopulations are dynamically adjusted to balance the exploration and exploitation of the search. We propose a constructive heuristic to generate initial subpopulations with different WIP levels, hybrid mutation and crossover operators, an evaluation method that can tackle infeasible individuals and a one-to-one greedy tabu selection method. Computational results on both benchmark instances and randomly generated instances show that our proposed hybrid DDE algorithm outperforms the basic DDE algorithm and can solve larger-size instances than the existing ε-constraint method.     

Scheduling a hybrid flowshop with batch production at the last stage

In this paper, we address the problem of scheduling n$n$ jobs in an s$s$-stage hybrid flowshop with batch production at the last stage with the objective of minimizing a given criterion with respect to the completion time. The batch production at stage s$s$ is referred to as serial batches by Hopp and Spearman where the processing time of a batch is equal to the sum of the processing times of all jobs included in it. This paper establishes an integer programming model and proposes a batch decoupling based Lagrangian relaxation algorithm for this problem. In this algorithm, after capacity constraints are relaxed by Lagrangian multipliers, the relaxed problem is decomposed based on a batch, unlike the commonly used job decoupling, so that it can be decomposed into batch-level subproblems, each for a specific batch. An improved forward dynamic programming algorithm is then designed for solving these subproblems where all operations within a batch form an in-tree structure and the precedence relations exist not only between the operations of a job but between the jobs in this batch at the last stage. A computational comparison is provided for the developed algorithm and the commonly used Lagrangian relaxation algorithm which, after capacity constraints and precedence relations within a batch are relaxed, decomposes the relaxed problem into job-level subproblems and solves the subproblems by using dynamic programming. Numerical results show that the designed Lagrangian relaxation method provides much better schedules and converges faster for small to medium sized problems, especially for larger sized problems.     

A new Lagrangian Relaxation Algorithm for scheduling dissimilar parallel machines with release dates

In this article we investigate the parallel machine scheduling problem with job release dates, focusing on the case that machines are dissimilar with each other. The goal of scheduling is to find an assignment and sequence for a set of jobs so that the total weighted completion time is minimised. This type of production environment is frequently encountered in process industry, such as chemical and steel industries, where the scheduling of jobs with different purposes is an important goal. This article formulates the problem as an integer linear programming model. Because of the dissimilarity of machines, the ordinary job-based decomposition method is no longer applicable, a novel machine-based Lagrangian relaxation algorithm is therefore proposed. Penalty terms associated with violations of coupling constraints are introduced to the objective function by Lagrangian multipliers, which are updated using subgradient optimisation method. For each machine-level subproblem after decomposition, a forward dynamic programming algorithm is designed together with the weighted shortest processing time rule to provide an optimal solution. A heuristics is developed to obtain a feasible schedule from the solution of subproblems to provide an upper bound. Numerical results show that the new approach is computationally effective to handle the addressed problem and provide high quality schedules.     

区间数可重入混合流水车间调度与预维护协同优化

针对加工时间不确定的可重入混合流水车间调度与预维护协同优化问题,构建以区间最大完工时间、区间总碳排放和区间总预维护费用为优化目标的集成调度模型.针对问题特性,通过设计改进的可能度计算方法,定义区间意义下解的Pareto占优关系.提出一种改进的离散鲸鱼群算法,通过同步调度与维护策略,实现制造与维护的联合优化;设计个体间距离计算策略,寻找“最近较优个体”;设计个体位置移动策略以及多邻域搜索策略,有效地平衡全局搜索和局部搜索,提高收敛精度.通过大量的仿真实验和结果对比分析,表明了所提出的算法对于求解区间数可重入混合流水车间调度和预维护协同优化问题的有效性和可行性.     

Real-time scheduling for reentrant hybrid flow shops: A decision tree based mechanism and its application to a TFT-LCD line

A reentrant hybrid flow shop, typically found in the electronics industry, is an extended system of the ordinary flow shop in such a way that there exist one or more parallel machines at each serial stage and each job has the reentrant product flow, i.e., a job may visit a stage several times. Among the operational issues in reentrant hybrid flow shops, we focus on the scheduling problem that determines the allocation of jobs to the machines at each stage as well as the sequence of the jobs assigned to each machine. Unlike the theoretical approach on reentrant hybrid flow shop scheduling, we suggest a real-time scheduling mechanism with a decision tree when selecting appropriate dispatching rules. The decision tree, one of the commonly used data mining techniques, is adopted to eliminate the computational burden required to carry out simulation runs to select dispatching rules. To illustrate the mechanism suggested in this study, a case study was performed on a thin film transistor-liquid crystal display (TFT-LCD) manufacturing line and the results are reported for various system performance measures.